We show that for any computably enumerable (c.e.) degree a and any low n–c.e. degree l (n ≥ 1), if l < a, then there are n–c.e. degrees a0,a1 such that l < a0,a1 < a and a0 ∨ a1 = a. In particular, there is no low maximal d.c.e. degree.

We show that there is a strong minimal pair in the computably enumerable Turing degrees, i.e., a pair of nonzero c.e. degrees a and b such that a ∩ b = 0 and for any nonzero c.e. degree x ≤ a, b ∪ x ≥ a.

Fixing an arbitrary point p ∈ CP and a triple (g, d, `) of nonnegative integers satisfying the inequality g ≤ (d+l−1 2 ) − (l 2 ) , we associate a natural Hurwitz number to the (open) Severi-type varietyWg,d,` consisting of all reduced irreducibke plane curves of degree d + l with genus g and having an ordinary singularity of order l at p (the remaining singular points of such curves being usua...

Great success has been achieved in the area of unsupervised domain adaptation, which learns to generalize from labeled source unlabeled target domain. However, most existing techniques can only handle closed-set scenario, requires both and have a shared category label set. In this work, we propose two-stage method deal with more challenging task open set where contains categories unseen Our fir...

The aim of unsupervised domain adaptation is to leverage the knowledge in a labeled (source) improve model’s learning performance with an unlabeled (target) domain—the basic strategy being mitigate effects discrepancies between two distributions. Most existing algorithms can only handle closed set (UCSDA), i.e., where source and target domains are assumed share same label set. In this article, ...

The existing iris recognition methods offer excellent performance for known classes, but they do not consider the rejection of unknown classes. It is important to reject an object class a reliable system. This study proposes open-set based on deep learning. In method, by training network, extracted features are clustered near feature centre each kind image. Then, authors build open-class outlie...